The stabbings happened around 1:20 a.m. MT on Tuesday at an address in the 100 block of Butler Crescent N.W., police said.
According to neighbours, the youths had been celebrating the last day of university classes with a fire in a home's backyard.
Three males were pronounced dead at the scene while two others who were taken to hospital in critical, life-threatening condition, and later died, officials said.
One other person suffered minor injuries.
All those who died were in their late teens to early 20s, police said.
The suspect fled on foot but police arrested him about 40 minutes later with assistance from the K-9 unit. Investigators are not looking for any more suspects.
The homicide unit is investigating.